# Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
3 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We study the following problem: Given $k$ paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension $d\geq 2$, there is a set of $d + 1$ paths that does not admit a monotone simultaneous geometric embedding.
Document type :
Preprints, Working Papers, ...

Cited literature [19 references]

https://hal.inria.fr/hal-01529154
Contributor : Olivier Devillers <>
Submitted on : Tuesday, May 30, 2017 - 2:01:41 PM
Last modification on : Friday, September 20, 2019 - 4:56:35 PM
Long-term archiving on : Wednesday, September 6, 2017 - 12:32:30 PM

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paths-embeddings.pdf
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### Identifiers

• HAL Id : hal-01529154, version 1

### Citation

David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, et al.. Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$. 2017. ⟨hal-01529154v1⟩

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